On the occurrence and role of SnO2, SnS and FeSn2 in coal hydroliquefaction experiments using tin-based catalysts

Mössbauer Spectroscopy, X-Ray Diffraction and Electron Microscopy were applied to the study of solid residues of coal hydroliquefaction, for which tin-based catalysts were used. In the general case hydroliquefaction runs were performed in the presence of added sulphur and of finely dispersed SnO₂ as a catalyst precursor. The only observed tin species were SnO₂ and SnS, the former with percentages higher than expected from XRD, due to its large f factor, the latter as a symmetric doublet, which suggests that any asymmetry should be ascribed to small particle sizes rather than to structure. When the S content was only that of coal and the catalyst precursor β-Sn, FeSn₂ occurred together with Sn sulfides and oxides, while no β-Sn was detected. The main catalytic role is ascribed to SnS.     

Simplicial normalization in the entire cyclic cohomology of Banach algebras

We show that the entire cyclic cohomology of Banach algebras defined by Connes has the simplicial normalization property. A key tool in the proof is the notion and properties of supertraces on the Cuntz algebraQ A. As an example of further applications of this technique, we give a proof of the homotopy invariance of entire cyclic cohomology.Address after 1st October 1995: Department of Mathematics, University of Exeter, North Park Road, Exeter EX4 4QE, U.K.     

Excision in Cyclic Type Homology of Frechet Algebras

It is proved that every topologically pure extension of Fréchetalgebras 0 I A A/I 0 such that I is strongly H-unital hasthe excision property in continuous (co)homology of the followingtypes: bar, naive-Hochschild, Hochschild, cyclic, and periodiccyclic. In particular, the property holds for every extensionof Fréchet algebras such that I has a left or right boundedapproximate identity.     

Möbius Transformations in Noncommutative Conformal Geometry

We study the projective linear group PGL ₂(A) associated with an arbitrary algebra A and its subgroups from the point of view of their action on the space of involutions in A. This action formally resembles M?bius transformations known from complex geometry. By specifying A to be an algebra of bounded operators in a Hilbert space H, we rediscover the M?bius group μ _ev (M) defined by Connes and study its action on the space of Fredholm modules over the algebra A. There is an induced action on the K-homology of A, which turns out to be trivial. Moreover, this action leads naturally to a simpler object, the polarized module underlying a given Fredholm module, and we discuss this relation in detail. Any polarized module can be lifted to a Fredholm module, and the set of different lifts forms a category, whose morphisms are given by generalized M?bius tranformations. We present an example of a polarized module canonically associated with the differentiable structure of a smooth manifold V. Using our lifting procedure we obtain a class of Fredholm modules characterizing the conformal structures on V. Fredholm modules obtained in this way are a special case of those constructed by Connes, Sullivan and Teleman. Received: 2 October 1997 / Accepted: 11 August 1998     

Property A, partial translation structures, and uniform embeddings in groups

We define the concept of a partial translation structure ona metric space X and show that there is a natural C*-algebraC*() associated with it, which is a subalgebra of the uniformRoe algebra C*_u(X). We introduce a coarse invariant of the metricwhich provides an obstruction to embedding the space in a group.When the space is sufficiently group-like, as determined byour invariant, properties of the Roe algebra can be deducedfrom those of C*(). We also give a proof of the fact that theuniform Roe algebra of a metric space is a coarse invariantup to Morita equivalence.     

K-theory and exact sequences of partial translation algebras

In an earlier paper, the authors introduced partial translation algebras as a generalisation of group C^?${\mathrm{C}}^{?}$-algebras. Here we establish an extension of partial translation algebras, which may be viewed as an excision theorem in this context. We apply this general framework to compute the K-theory of partial translation algebras and group C^?${\mathrm{C}}^{?}$-algebras in the context of almost invariant subspaces of discrete groups. This generalises the work of Cuntz, Lance, Pimsner and Voiculescu. In particular we provide a new perspective on Pimsner's calculation of the K-theory for a graph product of groups.     

D-Branes,RR-Fields and Duality on Noncommutative Manifolds

We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of T-duality as well as establishing a very general formula for D-brane charges. This formula is closely related to a noncommutative Grothendieck-Riemann-Roch theorem that is proved here. Our approach relies on a very general form of Poincaré duality, which is studied here in detail. Among the technical tools employed are calculations with iterated products in bivariant -theory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams.     

Chern Character for the Schwartz Algebra of p-Adic GL(n)

Let G denote the p-adic group GL(n), and let S(G) denote theSchwartz algebra of G. We construct a Chern character from theK-theory of the reduced C*-algebra of G to the periodic cyclichomology of S(G) which becomes an isomorphism after tensoringover Z with C.